Complete permutation polynomials from exceptional polynomials
Giovanni Zini · IRIS UNIMORE (University of Modena and Reggio Emilia) · 2017
We classify complete permutation monomials of degree q n − 1 q − 1 + 1 over the finite field with q n elements in odd characteristic, for n + 1 a prime and ( n + 1 ) 4 < q . As a corollary, a conjecture by Wu, Li, Helleseth, and Zhang is proven in odd characteristic. When n + 1 is a power of the characteristic we provide some new examples. Indecomposable exceptional polynomials of degree 8 and 9 are also classified.